How many images? Two mirrors at an angle
Stand a toy in front of one mirror, then between two mirrors hinged together, and count the images as you open and close the angle between them.
Core concept
Two plane mirrors at an angle θ form 360° ÷ θ − 1 images
Topic: Light
One plane mirror forms one image of an object, as far behind the mirror as the object is in front. Put two mirrors side by side and hinge them together, and the light can bounce from one mirror to the other before it reaches your eye. Each extra bounce makes an extra image, so you can see several copies of the object at once. The smaller the angle between the mirrors, the more times the light can bounce, and the more images you see. When the angle θ divides 360° exactly, the number of images is 360° ÷ θ − 1. A kaleidoscope uses mirrors at 60° to turn a few coloured beads into a beautiful pattern.
What you will learn
- Count the images formed by one plane mirror and by two plane mirrors at different angles.
- Use the rule: number of images = 360° ÷ angle − 1.
- Explain why closing the angle between the mirrors makes more images.
Before you start
- Know that a plane mirror forms an image as far behind the mirror as the object is in front.
- Know that a full turn is 360°.
Materials
- A small toy (or a coin, or a lit candle)
- A protractor
Equipment
- Two plane mirrors joined at one edge with tape, so they open like a book
Procedure
- Stand the toy in front of one mirror and count its images.
- Hinge two mirrors together, open them out flat (180°) and count again.
- Close the mirrors to 90° and then 60°, counting the images each time.
- Try more angles and look for a rule linking the angle and the number of images.
How this simulation is simplified
- The mirrors are perfect plane mirrors, and the toy stands on the line halfway between them.
- Only angles that divide 360° exactly are used, so every image can be seen clearly.